GROUP IV ELEMENTS IN 2D
STRUCTURES
Composition of the graduation committee
Chairman/secretary
Prof. dr. J. N. Kok
Supervisor(s)
Dr. ir. M. P. de Jong
Co-supervisor(s)
Prof. dr. ir. H. J. W. Zandvliet
Committee Members
Prof. dr. ir. G. Koster
Dr. ir. A. Y. Kovalgin
Prof. dr. T. Banerjee
Prof. dr. P. K. J. Wong
Dr. A. Fleurence
This work was financially supported by the Netherlands Organization for
Scientific Research (NWO). Support is also acknowledged from the
following institutes for having provided synchrotron beam time: ISA
(Denmark), UVSOR (Japan), SOLEIL (France) and Photon Factory (Japan).
Printed by: Ipskamp
ISBN: 978-90-365-5025-3
DOI: 10.3990/1.9789036550253
© 2020 Michal Witold Ochapski, The Netherlands. All rights reserved. No
parts of this thesis may be reproduced, stored in a retrieval system or
transmitted in any form or by any means without permission of the author.
Alle rechten voorbehouden. Niets uit deze uitgave mag worden
vermenigvuldigd, in enige vorm of op enige wijze, zonder voorafgaande
schriftelijke toestemming van de auteur.
GROUP IV ELEMENTS IN 2D STRUCTURES
DISSERTATION
to obtain
the degree of doctor at the Universiteit Twente,
on the authority of the rector magnificus,
Prof.dr. T.T.M. Palstra,
on account of the decision of the Doctorate Board
to be publicly defended
on Wednesday 2 September 2020 at 14.45 hrs
by
Michał Witold Ochapski
born on 21 February 1990
This dissertation has been approved by:
supervisors
Prof. dr. M.P. de Jong (supervisor)
i
TABLE OF CONTENTS
Introduction to 2D materials ... 1
1.1 Introduction ... 1
1.2 Surface science techniques ... 2
1.2.1 Low energy electron diffraction – LEED ... 3
1.2.2 Scanning tunneling microscopy – STM ... 6
1.2.3 Photoelectron spectroscopy – PES ... 8
1.3 Outline ... 11
References ... 11
Substrates feasible for epitaxial growth of stanene ... 15
2.1 Introduction ... 15
2.2 Structural stability ... 16
2.3 Properties ... 18
2.4 Substrates ... 18
2.4.1 Substrates with reported realization of epitaxial of stanene... 18
2.4.2 Substrates theoretically predicted to support epitaxial stanene ... 26
2.5 Conclusions ... 33
References ... 34
Epitaxial Sn on silicene terminated ZrB2 ... 43
3.1 Introduction ... 43
3.2 Methods ... 44
3.2.1 Silicene-terminated ZrB2(0001) thin films on Si(111) ... 44
3.2.2 Sn deposition ... 44
3.2.3 Measurement methods ... 45
3.3 Results and discussion ... 45
3.3.1 Silicene on ZrB2 ... 45
ii 3.3.3 350 – 500˚C Regime ... 54 3.3.4 500 – 650˚C Regime ... 59 3.4 Conclusions ... 65 References ... 67 Epitaxial Sn on MoS2 ... 75 4.1 Introduction ... 75 4.2 Methods ... 75
4.3 Results and discussion ... 76
4.4 Conclusions ... 83
References ... 83
Li intercalation into multilayer graphene with controlled defect densities ... 87
5.1 Introduction ... 87
5.2 Methods ... 88
5.3 Results and discussion ... 88
5.4 Conclusions ... 95 References ... 95 Outlook ... 99 Summary ... 103 Samenvatting ... 105 List of publications ... 109 Acknowledgements ... 111
1
CHAPTER 1
Introduction to 2D materials
1.1 Introduction
The discovery of graphene opened a new field in the physics of solid matter, focusing on two dimensional (2D) materials [1]. The newly obtained material turned out to have very unusual properties, the most interesting in its electronic aspect. Graphene shows linear dispersion around the Fermi level – a Dirac cone [2]. This makes the electrons velocity in graphene independent of energy, i.e. they behave as if they have no mass. It also exhibits very high carrier mobility [3]. Graphene came into existence at a similar time with the development of another new branch of (theoretical) solid-state physics, investigating topological states of matter [4]. What made the material really “famous” was that it is predicted to be a promising candidate for a variety of exotic topological properties [5]. From there, it has quickly grown to become one of the major research directions in today’s field of materials science.
However promising, over 15 years of research on graphene has shown that some major obstacles on the way to utilizing its electronic properties are very hard to overcome. Even though theoretically possible, non-trivial topological effects are inaccessible for experimental physics, due to the extreme conditions in which those effects appear. The reason for this is the lack of a bandgap, which also hampers the application of graphene in semiconductor devices. The attempts of modifying graphene’s electronic structure in order to open a significant bandgap with several techniques, like adsorbates, stress, external fields and even shape had only limited success. Hence, the attention of the community turned to other 2D materials, where this major problem would be easier to tackle. There are several directions including transition metal dichalcogenides and other
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layered Van der Waals materials, many of which are semiconductors with significant band gaps. However, these materials are not atomic monolayers in single layer form (see Fig. 1.1c), and their properties differ significantly from those of graphene. Nonetheless these materials are still interesting (for example due to the band gap dependence on the number of layers in some of them) and widely studied. Another reason is their feasibility of being stacked together in heterostructures with potentially new properties.
Another branch of the 2D materials field evolved from a graphene-inspired idea of elemental honeycomb atomic monolayers. Such materials would mimic graphene in its properties much more accurately, and many of them seem to be able to outshine graphene in the field of electronics. The main focus of this thesis is on such elemental 2D materials from Group IV – silicene, germanene, and in particular – stanene (see Fig. 1.1b). The properties of stanene are discussed in some detail in chapter 2.
Fig. 1.1 Atomic models of various 2D materials. a) Graphene is an elemental 2D material with an atomically flat honeycomb lattice. Reproduced from [6]. b) The lattice of stanene as well as several other elemental 2D materials exhibit a degree of buckling [7]. c) MoS2 is a Van der Waals layered material with (when viewed from the top) honeycomb lattice that consist of three covalently bonded atomic sheets (S, Mo, S). Reproduced from [8].
1.2 Surface science techniques
Due to their atomically thin structure, 2D materials are ideally suited for probing with surface science techniques that allow for experimental characterization of the surface properties of materials. Many of such techniques require high cleanness of the surface and are sensitive to contamination due to the nature of 2D materials. While graphene itself is quite inert to ambient conditions, others, and in particular materials discussed in this thesis, are by themselves very sensitive to contamination and possible
3 degradation or decomposition due to atmospheric pressure and contact with more reactive elements. To avoid these problems, surface science techniques are performed in ultra-high vacuum (UHV) conditions, with pressure of the order of 10-10 mbar. Many
2D materials are also prepared in UHV and then measured in-situ. In this work, all the experimental process, comprising sample preparation and measurement were performed
in-situ. The sample preparation techniques were thermal evaporation and annealing.
Evaporation is a physical vapor deposition (PVD) technique. In thermal evaporation, the material to be deposited is put into a (ceramic or an inert metal) crucible which is radiatively heated, until the material evaporates. The sample is then kept in the vicinity of the source, so the evaporating material can adsorb on the sample surface. Annealing is a technique used to increase the temperature of the sample in order to increase the degree of structural order, achieve a phase transition, or stimulate some chemical reaction. In this work, several annealing techniques were used – radiative, e-beam and direct current heating. Radiative annealing is the simplest one, where a filament is heated up by direct current and put in close vicinity of the sample. In e-beam annealing, the sample is heated up by electron bombardment from a hot filament at high voltage (either the sample or the filament can be at high voltage). This requires conducting samples, and should be done such that the electrons bombard the backside of the sample to avoid damage. Finally, DC heating heats the sample by passing a DC current through it. For this method to be effective, the samples need to be quite resistive (otherwise extremely high currents are required). It works well for (doped) Si wafers, which are commonly used substrates in the field. As for measurement techniques, we utilized several complementary surface science techniques which allow for detailed characterization of structural and electronic aspects of the studied samples.
1.2.1 Low energy electron diffraction – LEED
Low energy electron diffraction is an experimental technique used for determination of the structural properties such as size, symmetry and rotational alignment of unit cells present on the surface. In particular, it is often used to study surface lattices of adsorbates. Fig. 1.2a shows a schematic illustration of a LEED system. In ultra-high Vacuum (UHV), the electrons emitted from a hot filament are accelerated to a predefined energy onto the sample surface by an electron gun. The interference of the incident electrons scattered on the crystal lattice of the sample results in a diffraction pattern, which can be observed on a fluorescent screen. Several grids are typically located between the screen and the sample, to filter the inelastically scattered electrons.
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LEED is a very useful and fast tool to examine if a deposited material formed an ordered structure on the surface of a substrate.
The principle behind LEED utilizes the wave-like nature of electrons. Electrons, according to the de Broglie relation, have a wavelength 𝜆𝑒 of:
𝜆𝑒= ℎ/𝑝 = ℎ/√2𝑚𝑉𝑒, (1.1)
where h is the Planck constant and p is the electron momentum, m is the electron mass,
e is the electron charge, and V is the acceleration voltage. This equation gives a relation
between an applied voltage and the electron wavelength. Based on this concept there are two fundamental requirements that 𝜆𝑒 needs to fulfill to be useful in LEED
technique: (i) it needs to be small enough to be diffracted by an atomic lattice and (ii) the energy of the electrons needs to be such that the inelastic mean free path 𝜆𝐼𝑀𝐹𝑃 of
the electron is minimized. 𝜆𝐼𝑀𝐹𝑃, in simple words, is the average distance which an
electron can travel through a material before it is scattered inelastically (see Fig. 1.2c). These two criteria are fulfilled when the energy of the electrons is between 20 and 400eV. In this range, the electron diffraction pattern can be observed and the penetration depth is low enough to probe only the outermost atomic layers.
The incident electrons are emitted from the electron gun by a cathode filament and focused by a set of electrostatic lenses. Upon reaching the surface the electrons scatter elastically from the atomic lattice of the sample. The diffracted electron waves that interfere constructively obey the Bragg equation, which is of the form (see Fig. 1.2b)
𝑛𝜆𝑒= 𝑑 sin𝜑, (1.2)
where 𝑛 is an arbitrary integer, 𝜆𝑒 is the electron wavelength, d is interatomic distance
in the lattice of the sample and 𝜑 is the angle between the incident and scattered electron “ray”. The interaction between scattered electrons and atomic lattice is most conveniently described in terms of reciprocal space. For an incident wave number k0 =
2π/λ0 and the scattered one k = 2π/λ, the condition for constructive interference is given
by the Laue condition, which is simply a reciprocal space equivalent of the Bragg equation. This representation is readily observed on a so-called Ewald sphere (see Fig.
5 1.2d). The diffraction pattern observed on the fluorescent screen is a direct image of the reciprocal lattice of the surface.
Fig 1.2: a) Diagram of a LEED system. Reproduced from [9]. b) Electron diffraction process. Reproduced from [10] c) Inelastic mean free path universal curve. Note that the electrons within 20 – 200 eV range have λIMFP < 1 nm. Reproduced from [11] [12]. d) Exemplary diffraction pattern and corresponding Ewald sphere. Reproduced from [13]
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1.2.2 Scanning tunneling microscopy – STM
Scanning tunneling microscopy (STM) is an experimental technique to characterize the topography of the sample surface. The experimental setup consists of a metal tip (the most common are Pt/Ir and W tips) that is put in nanoscopic vicinity of the sample – usually about 1 nm away. When a bias voltage is applied between the sample and the tip, a tunneling current can be detected. In a one-dimensional tunneling problem this current is given by: [14]
𝐼 ∝ 𝑒−2𝜅𝑧, (1.3)
where I is the tunneling current, 𝑧 is the tip-sample distance and κ is the decay constant for the wave function in a potential barrier. Therefore, such current depends exponentially on the barrier width, which corresponds to the tip-sample distance 𝑧. Only conducting and semiconducting samples are feasible for being studied by this method, since the tunneling current needs to be detected and controlled. The tip is mounted to a piezo-element that allows the tip to move in 3 directions with respect to the sample surface. An electronic feedback loop keeps the tunneling current constant, by varying z. In that way, in the so-called constant current mode, the tip can scan the surface in the
x-y plane and image the “topographx-y” of the sample (bx-y plotting the variation of 𝑧). One should keep in mind however, that since an electronic current is used to scan, what is really measured is also strongly dependent on the local density of states (DOS). The STM signal is therefore a mixture of electronic and topographic components. This method enables measurements with atomic resolution, making it possible to detect individual atoms.
Another way to utilize the such system is scanning tunneling spectroscopy (STS). The technique takes advantage of the fact, that in stable temperature conditions and with featureless density of states of the tip, the local density of states of the sample 𝜌𝑆 is
proportional to the deritavite of the tunneling current over the bias voltage:
𝑑𝐼
𝑑𝑉~𝜌𝑆. (1.4)
This technique allows for the measurement of local density of states on the sample, and in its more advanced version to make dI/dV maps of the sample surface.
7 Fig. 1.3: a) Schematic illustration of the STM system with typical orders of magnitude of bias voltage, tip-sample distance and tunneling current. Dark spheres represent atoms in the sample/tip. Adapted from [15]. b) Microscopic view of STM imaging mechanism. The tunneling conductance is generated by the overlap of the tip state with the atomic-like states on the sample. Reproduced from [17].c) Schematic energy diagram for the tunnel junction between a metallic tip and an adsorbate-covered metal surface. The left (right) junction corresponds to a negative (positive) bias on the sample to permit tunneling from occupied states of the sample (tip) into empty states on the tip (sample). Only states within the energy window ΔE can contribute. φs and
φt are the local work functions (barrier heights) for the sample and tip, respectively, whereas z is the tunnel gap width. Reproduced from [16].
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1.2.3 Photoelectron spectroscopy – PES
Photoelectron spectroscopy is a technique that gives insight into the chemical composition and electronic (band) structure of the sample surface. The technique allows to identify elements present on the surface, as well as gives information about chemical bonding. It also allows for estimation of layer thickness for ultrathin films, provided that the sample composition is well known. PES is based on the famous photoelectric effect, discovered by Hertz and explained by Einstein. By absorbing photons with energy hν, electrons can gain enough energy to escape the potential well of the system to which they are bound (a metallic solid in the examples below). This can be done at the cost of overcoming the barrier formed by the electron energy level with respect to the Fermi energy – the binding energy EB – and the work function of the surface 𝜙, according to
the equation:
𝐸𝑘 = ℎ𝜈 − 𝐸𝐵− 𝜙. (1.5)
The remaining energy is the kinetic energy EK of the photoelectron. In PES, significant
interest is put on the core levels – energy levels far below the Fermi energy. Due to the fact that each element has specific binding energies of its core levels, PES is an excellent tool for chemical characterization of the sample (the technique was originally coined “Electron Spectroscopy for Chemical Analysis”, in short ESCA, by its inventor Siegbahn). The signal comes from only the outermost layers, which is connected to the aforementioned electron inelastic mean free path – λIMFP (see Fig. 1.2c), which can be
varied with the photon energy (λIMFP depends on EK). The obtained signal intensity is
proportional to the number of emitted electrons vs binding energy. At binding energies corresponding to the core levels of elements present on the surface there will be peaks in intensity. The intensity, position and shape of the peaks give insight, among others, into the abundance, chemical environment, and the degree of disorder in the chemical environment of a given element in the sample.
The PES system consists of a photon source, and a detector (see Fig. 1.4a). In lab-based systems the photon source typically emits X – rays (hence the method is often called X – ray photoelectron spectroscopy – XPS), generated by bombarding a metallic anode with high-energy electrons. Usually only a few pre-defined photon energies are available. To overcome that limitation, as well as to achieve higher energy resolution, synchrotron radiation is used for high-quality PES measurements. This allows for a much broader range of well controlled photon energies. Fig. 1.4a illustrates
9 schematically the geometry of the PES system. The incident photons get absorbed by the core level electrons, which escape the sample and then are accelerated to the detector, which measures the intensity (number of detected electrons in a certain time interval) at each kinetic energy.
Fig. 1.4: a) (AR)PES experimental set up, the polar and azimuthal directions are specified by the angles ϑ and 𝜑, respectively. b) The photoelectron energy distribution (right), with respect to the energy levels in a solid (left). Reproduced from [18] [11]. c) Energy-conservation diagram of the photoemission process. d) Momentum parallel to the surface of photoelectrons is conserved during the photoemission process. Reproduced from [19].
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Angle-resolved photoelectron spectroscopy (ARPES) is a more sophisticated technique based on the same principle as PES. The experimental system for ARPES is identical to that used in PES, except the detector collects additionally the information about the exit angle (ϑ in Fig. 1.4a) of the electrons. This allows to image a band structure of the sample surface.
In addition to the photoelectric effect, ARPES makes use of two very basic concepts – the energy of the photon – electron system should be conserved and so should be the momentum. Imagine an electron in an initial state 𝐸𝑖 [19]. By absorbing a photon with
the energy ℏ𝜔 it is excited to the state at the energy 𝐸𝑓. From energy conservation we
have:
𝐸𝑓 = ℏ𝜔 + 𝐸𝑖. (1.6)
In the case of photoelectron, the excited state is a free-electron state in vacuum, for which the energy is expressed by
𝐸𝑓 = 𝐸𝑘+ 𝑊, (1.7)
where 𝐸𝑘 is the kinetic energy and 𝑊 – the work function of the sample. The parallel
component of the momentum is conserved in the whole process (the photon has negligible momentum), due to translational symmetry of both the crystal structure in the surface plane as well the vacuum. The parallel component of the photoelectron momentum can be expressed by the formula:
𝑘∥= √2𝑚𝐸𝑘 ℏ 𝑠𝑖𝑛𝜗 = √2𝑚(𝐸𝑖+ℏ𝜔−𝑊) ℏ 𝑠𝑖𝑛𝜗, (1.8)
where, 𝑘∥ is the in-plane component of the momentum 𝑘, 𝜗 is the angle between the
direction of the momentum 𝑘 and a vector normal to the sample surface plane (Fig. 1.4a). This relation allows for obtaining a slice of the energy dispersion relation 𝐸𝑘(𝑘∥)
in the 𝒌∥= 𝒌𝑥+ 𝒌𝑦 direction in the sample. In practical applications, only the high
symmetry directions of 𝒌∥ in the Brillouin zone are investigated. There is also a
possibility for imaging the whole Fermi surface, by recording slices at different angles 𝜗 and 𝜑 . Some modern systems, with a (near) 180 ̊ acceptance angle for emitted photoelectrons, are able to perform such a measurement without having to rotate the sample at all.
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1.3 Outline
This thesis is a contribution to the 2D materials field, with a particular focus on group IV elemental 2D materials. By utilizing several complementary surface science techniques we investigated the formation of ordered structures in 2D regime and interactions between these materials and various substrates. In chapter 2, we review and systematize the experimental aspects of the knowledge about substrates suitable for epitaxial growth of stanene. Chapters 4 and 5 presents our work on growth of epitaxial Sn layers on different substrates – silicene terminated ZrB2 (chapter 4) and MoS2
(chapter 5). Finally, Chapter 5 shows an investigation on Li intercalation in between graphene sheets, focusing on how defects may influence the intercalation capacity of multilayer graphene.
References
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[3] K. I. Bolotin et al., “Ultrahigh electron mobility in suspended graphene,”
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heterostructures,” J. Phys. Appl. Phys., vol. 46, no. 50, p. 505308, Dec. 2013, doi: 10.1088/0022-3727/46/50/505308.
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[14] P. K. Hansma and J. Tersoff, “Scanning tunneling microscopy,” p. 24, 2014. [15] H. Yaghoubi, “The Most Important Maglev Applications,” J. Eng., vol. 2013, pp. 1–19, 2013, doi: 10.1155/2013/537986.
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CHAPTER 2
Substrates feasible for epitaxial
growth of stanene
2.1 Introduction
After the discovery of graphene, a two-dimensional (2D) material (single layer of C atoms) with exceptional electronic properties, interest in other 2D materials has skyrocketed. One of the most attractive properties of graphene is that its charge carriers behave as massless Dirac fermions,[1] which leads to exceptionally high mobility values on the order of 105 cm2V-1s-1.[2] A two-dimensional (2D) topological insulator
phase, the quantum spin hall insulator (QSHI), has also been predicted to exist in graphene [3]. The spin-orbit coupling (SOC) that lies at the origin of this state is very weak though, such that the effects may only be observed at extremely low temperatures [4]. Other elements of group IV, e.g. Si, Ge and Sn, exhibit the same valence electronic configuration as C, leading to similar band structures in bulk crystals, while the SOC increases strongly with atomic number Z, roughly as Z4. This has led to enormous
interest in graphene-like, 2D materials of group IV elements. Stanene, along with graphene, silicene and germanene belongs to this group IV 2D materials family. It is a 2D monolayer of Sn in a honeycomb, graphene-like, lattice. Stanene took its name from the latin name for tin – stannum [5].The interest in stanene can be regarded as a follow-up of the development of the elemental 2D materials field, in particular the research on the feasibility of the lighter group IV elements – Si and Ge – to form their own 2D structures – silicene and germanene. The investigation of stanene has started in 2013
16
with a seminal paper by Xu et al. [5] Another early report of the properties of free standing stanene was by Broek et al. in 2014 [6].
2.2 Structural stability
Like the other novel 2D materials from group IV, stanene has a buckled honeycomb lattice structure with 2 atoms in the primitive cell. The lattice constant has been initially reported to be 4.62 – 4.68 Å [5] [6]. Sn atoms are relatively large in comparison with the lighter group IV elements. This gives rise to two extraordinary effects, which make stanene a very interesting material. One is buckling of the lattice, and the other is strong spin-orbit coupling. The repulsion forces between atoms are relatively strong which results in larger bond lengths that prevent the atoms from forming strong π bonds. Sn atoms are pushed in the out-of-plane direction, effectively buckling the lattice and deviating the structure away from pure sp2 hybridization. The buckling corresponds to
a mixed sp2 – sp3 hybridization. This effect has far reaching consequences and is the
main characteristic that distinguishes stanene from graphene. Similar effects are found in silicene and germanene [7]. However, in case of Sn atoms, as the largest among the three, the effects and resulting phenomena are the strongest.
The other distinguishing effect present in stanene is non-negligible spin-orbit coupling (SOC) which makes it a topological insulator [5] [8], analogous to the initial prediction of a QSHI state by Kane and Mele [3]. The SOC is much stronger than in C, Si or Ge, due to the larger nuclear charge of Sn atoms. Therefore, the SOC-induced gap at the K and K’ points, which lies at the heart of the formation of the QSHI state, is much larger and has been predicted to surpass the thermal energy even at room temperature. In a free-standing stanene, similarly to silicene and germanene, there are 2 energy minima classified according to buckling height Δ as high (HB) and low (LB) buckling of the lattice. Calculations of stability suggest that, in contradiction to silicene and germanene, the HB phase is the global minimum with lattice constant of 3.4 Å [9]. However, that phase is metallic. Hence the interest is mainly in the LB phase, which is predicted to have non-trivial topological properties [5]. In the LB phase, stanene has the lattice constant λ = 4.68 Å and buckling height Δ = 0.85 Å [5]. Fig. 2.1a and 2.1c show the atomic structure of free-standing LB stanene as well as its predicted structural parameters. Another form of a free-standing monolayer of Sn is dumbbell stanene, which is also calculated to be more stable than the LB phase [10]. This structure is
17 however far from the graphene-like configuration hence it is not going to be discussed further in this review.
Fig. 2.1. a) Top and side view of the stanene lattice with primitive cell indicated by black rhombus. b) Electronic band structure of stanene without (black dash-dotted lines) and with (red solid lines) spin-orbit coupling. The inset shows a zoomed-in energy dispersion near the K point. The Fermi level is indicated by the dashed line. b) Comparison of the structural and electronic parameters of group IV elemental 2D materials. From the top: lattice constant a, bond length d, buckling parameter Δ, Fermi velocity vF, effective masses of Dirac particles m*, Electronic band gap Eg. Electronic quantities are derived from hybrid HSE06 calculations. The GGA results are given in parentheses. Eg and m* are calculated with the inclusion of SOC (without SOC, Eg =
18
2.3 Properties
Many theoretical studies have been done on a variety of stanene properties. Here we shortly summarize its most important electronic characteristics, as these draw most attention to the material. The two most important features recognized in its band structure are: (i)preservation of the linear energy dispersion (Dirac cones) at the K and
K’ points, which signalizes high carrier mobility, as well as (ii) a significant SOC –
induced band gap of 100 meV [5] which predicts stanene to be a topological insulator and allows for a quantum spin Hall effect (QSHE) to occur at room temperature [16]. This seems to be the largest non-trivial band gap for a free-standing 2D material of group IV, as Pb - the heaviest group IV element - in its 2D form is a metal [5]. The bandgap can be further tuned and enlarged by various techniques, such as chemical functionalization [11], strain [12] [13] or electrical field [14] [15] up to 0.3 eV [5]. Fig. 2.1 b-c give insight in stanene’s electronic properties.
2.4 Substrates
Experimental realization of stanene (as well as silicene and germanene) is problematic, due to sp3 hybridization being energetically more favorable than sp2. As a result, there
is no layered form of Sn analogous to graphite in nature. The solution to this obstacle is synthesis on a substrate that would support formation of a Sn monolayer. The main challenge in this approach is the choice of a suitable substrate. There are a few properties that a substrate should poses to be a promising candidate. First of all, the stanene – substrate heterostructure must be stable. The stability is ensured in 2 ways – hexagonal/honeycomb symmetry of the outermost layer of the substrate and small lattice mismatch, in order to minimize the strain in the Sn layer. Secondly, the electronic properties of free standing stanene have to be preserved. To achieve this, preferable substrates must have a band gap as well as interact weakly (via Van der Waals forces) with the 2D material. Therefore, layered semiconductors/insulators with matching lattice constants would be perfect candidates a priori.
2.4.1 Substrates with reported realization of epitaxial of stanene
Several substrates have been examined theoretically for their feasibility to support stanene and preserve, or possibly even enhance, its properties. We note in passing that Sn growth on various substrates has been studied for a long time. Only recently however, thanks to the rise of graphene and the prediction of the exotic properties in
19 analogous 2D materials, the attention was directed to the quantum physical properties of Sn sheets.
The first report calling an epitaxial multilayer of Sn "stanene” has been reported in 2015 by Zhu et al. [25]. The Sn layer was epitaxially grown on Te-terminated bismuth telluride (Te-Bi2Te3) (see Fig. 2.1d). The growth was characterized by the
Vollmer-Weber mode (island growth).While the structural properties were in close accordance with the predicted values, the electronic band structure was strongly influenced by the substrate. The report opened the field of epitaxially grown stanene-like structures. Motivated by that successful experimentally realized growth, systematic DFT calculations of the system by Zhang et al. suggested that growth on the Te-terminated Bi2Te3 surface follows a partial-layer-by-partial-layer (PLBPL) growth mode,
characterized by short-range repulsive pairwise interactions of the Sn adatoms. They
proposed that Bi2Te3 pre-covered with a Bi bilayer would support the
nucleation-and-growth mechanism, strongly favoring single crystalline stanene [26]. Finally, a critical view on the possible growth of stanene with its expected properties on this substrate was signaled recently by Li et al. [27]. In their investigation of the electronic band structure of that system by XPS and ARPES, they showed a significant interfacial chemical interaction between Sn atoms and Bi2Te3. The presence of this interaction,
leading to Sn – Te chemical bonds in the stanene/Bi2Te3 system, casts doubts on the
feasibility of this substrate for stanene growth.
Indium antimonide(InSb) has been regarded as a promising candidate for the growth of Sn sheets [18] [19] [20]. Barfuss et al. [21] reported the possibility to obtain a Quantum 3D topological phase in strained α-Sn on this substrate. They also predicted the QSHE in a Sn monolayer on this substrate. Another argument for the feasibility of this material to support a stanene layer was provided by Tang et al. [22]. In their paper they investigated dumbbell stanene on the InSb(111)-(2 x 2) thin film and concluded that, despite strong coupling between the substrate and the Sn layer, the topologically non-trivial properties persist in the hybridized structure, such that DB stanene is a 2D TI without inversion symmetry. Finally Xu et al. [23] reported on stanene epitaxially grown on InSb(111)B (Sb terminated) (see Fig. 1g ). ARPES measurements of the pristine films and K-doped films demonstrate a large gap of 0.44 eV at the Brillouin zone center. The size of that band gap is larger than that expected for free-standing stanene, because of the electronic coupling between the Sn and InSb conduction band states [23]. Such a large band gap suggests the exotic properties in this structure to be accessible even above room temperature (For T = 300 K the thermal energy kBT is 0.25
20
An interesting experiment with a similar substrate was undertaken by Gou et al. [24], who report on an epitaxially grown stanene film on an antimony Sb(111) substrate (see Fig. 2.1f ). The significant stress, that the stanene layer undergoes, widens the bandgap at the K points to 0.2 eV, which is twice as big as the predictions for the free-standing material. However, multiple bands cross the Fermi level at the Γ point making stanene metallic. A systematic investigation with STS proved that the stanene band structure can be tuned with strain.
In their study from 2018, Zang et al. [28] report on stanene grown on Sr-doped lead telluride (Sr-PbTe(111)). The Sn layer was unintentionally passivated by H, despite being kept in an ultra-high vacuum (UHV) environment. While the obtained stanene seemed to be a trivial insulator, the authors suggest activating the topological properties by streching its lattice constant, which, as they further imply, can be done using similar substrates, like EuTe, SrTe, BaTe with larger lattice constants. At about the same time, PbTe-covered Bi2Te3 was used by Liao et al. to grow few-layer stanene films, which
revealed novel superconducting behaviors controlled by the number of Sn layers [29]. After the successful growth of silicene on Ag(111), this became another candidate substrate for the possible growth of monolayer Sn. Ag was one of the metals investigated in theoretical work of Guo et al. [35] about the interfacial properties of stanene on various metals. They concluded that, while stanene is structurally stable on Ag and some of the other metals examined, it undergoes metallization on all of them. Further theoretical insight into the structural stability of the stanene/Ag(111) system was given by Gao et al. [36]. They showed that there are four stable reconstructions which could revert to the free-standing structure upon removal of the Ag substrate. They suggested that it is a good candidate for a proof-of-principle transistor, similarly to the silicene-made device, which was made by etching away Ag without destruction of the overlayer [37]. Inspired by theory, Yuhara et al. [30] reported on the growth of large area planar Sn-sheets on Ag(111) (see Fig. 2.1a ). Upon deposition of 1/3 ML, an Ag2Sn
alloy is formed. Further deposition gave rise to an additional planar layer of Sn. ARPES measurements identified the heterostructure as metallic. The formation of an alloy layer poses a question about the possibility to remove the substrate in order to obtain a free-standing material, like in the case of silicene. An attempt to solve this problem was undertaken by Luh et al. [38] who performed a temperature dependent study on Sn growth on Au(111). Inspired by the previously calculated large diffusion coefficient for Sn on Ag (111) at 300 K they conducted Sn deposition at lowered temperatures in order to prevent forming an alloy. However, they failed to achieve this even at temperatures as low as 96 K. The question if there is an alloy-free regime below that temperature in the Sn/Ag systems remains unanswered for now.
21 A similar example of a planar Sn layer was reported on Cu(111) by Deng et al. [33] (see Fig. 2.1e ). The method used to prevent forming an alloy was deposition at low temperature, in this case 200 K. The obtained structure was an atomic layer of Sn in a planar honeycomb lattice with no buckling, which was named “ultraflat stanene”. The strong interactions with the substrate and the lattice stretching stabilized the zero – buckling geometry, creating a honeycomb lattice. This lattice was characterized by an s
– p band inversion and a bandgap at the Γ point induced by SOC. Green’s function
calculations confirmed the topologically derived boundary states suggested by scanning tunneling spectroscopy ( STS ) measurements. The structure is stable up to 240 K. It is also important to note that even though there was a finite bandgap in the stanene layer, ARPES measurements showed that the system was overall metallic, due to metallic bands from the substrate.
Nigam et al. [39] investigated the Au(111) surface as a potential candidate for a substrate supporting stanene via density functional theory ( DFT ) calculations. The Sn layer prefers a planar over a buckled structure, which was explained by the participation of Sn – pz orbitals in bonding with Au. This is contradictory to the work by Guo et al.
[35], who in their calculations obtained buckled stanene on Au(111) with a buckling parameter almost twice bigger than in the case of free-standing stanene. The authors realized this discrepancy and suggested different Van der Waals corrections considered in the two reports [35] as the possible reason. Experimental realization of stanene on Au(111) was achieved by Liu et al. [40] The deposited Sn atoms first formed a surface Sn-Au alloy, with a coverage-dependent structure. Upon further deposition, above a critical coverage, the Au-Sn alloy was converted into a strongly buckled, disordered honeycomb lattice of epitaxial stanene. DFT calculations and STM images suggest strong tensile strain in the layer. Maniraj et al. [31], after their initial report on the same alloy [41], also reported on stanene formation on Au(111) (see Fig. 2.1b). Their ARPES investigation showed that the band structure of the Sn/Au superstructure is dominated by a linearly dispersing band centered at the Γ point, corresponding to a high Fermi velocity and a spin texture of a three-dimensional topological insulator.
Glass et al. investigated silicon carbide (SiC) substrates and reported the first realization of a triangular Sn lattice on SiC(0001) [45]. STM revealed the structure of the Sn lattice, which was reproduced in DFT calculations. DFT predicted a Sn-related band to cross the Fermi level, in the middle of a large band gap. Additional UPS measurements suggest a Mott-Insulating state. Encouraged by this promising result, Matusalem et al. [46] showed in their calculations that the passivation of the substrate and Sn layer in the stanene/SiC system results in quasi freestanding overlayers, with the presence of linearly dispersing Dirac-like bands in the band structures. They also identified the
22
configuration in which stanene conserves its topological character. Another variation, proposed by the same group was a graphene-covered SiC substrate [47]. In this case, while the Dirac cone is conserved, the authors report on strong charge transfer from stanene to graphene, which makes the topology of the system unclear. The possibility of substrate engineering was significantly explored by Di Sante et al. [48], who analyzed the influence of an elemental buffer layer on the stanene/SiC system. The buffer layers they examined were elemental Group III and V lattices. The goal was to protect the QSHI state in stanene. They chose atoms which have their bonding and antibonding states energetically far away from the chemical potential in order to minimize the detrimental staggered potential (due to lifting sublattice degeneracy). The analysis made them propose P and As as the best candidates for buffer layers. While other attempts focused on adding additional layers to tune the substrate, Ferdous et al. [49] investigated the properties of a stanene/SiC heterobilayer (see Fig. 2.3a). That system manifests a wide band gap up to 160 meV at the K point with a well-preserved Dirac cone. A closer look at the topological properties of stanene on SiC was undertaken by Li [50]. In this calculations stanene was stabilized by the strong interfacial bonding. This resulted in quadratically dispersing (non-Dirac) topological states at the Γ point, constructed of stanene’s px,y instead of the pz orbitals.
23 Fig. 2.2: (a-f)Selected large area and high resolution STM images of epitaxial stanene grown on: a) Ag2Sn surface alloy b) Au (111) c) Bi (111) d) Bi2Te3 e) Cu (111) f) Sb (111) g) Calculated (left) and measured with ARPES(right) band structure of stanene on InSb. h) HRTEM image of a free-standing Sn layer showing a hexagonal lattice. Reproduced from a) [30] b) [31] c) [32] d) [25] e) [33] f [24] g) [23] h) [34].
24
While epitaxial growth is the common way to approach synthesis of stanene, Saxena et
al. [34] took a different path and reported growing a freestanding few-layer stanene
film, obtained by impinging pulses from a tunable Ti:Saphire ultra-fast femto-second laser onto a target in a liquid medium (see Fig. 2.1h). They performed a series of structural studies which seem to confirm the claim, however no electronic properties measurements have been reported so far. Their further report confirms stanene’s structural signature in optical measurements [51].
Reports on experimentally realized growth of silicene [52] [53] and germanene [54] on molybdenum disulfide (MoS2) gave hopes for utilizing the material as a substrate also
for epitaxial synthesis of stanene. Liang et al. [55], Xiong et al. [56] and Ren et al. [57] (see Fig. 2.3b ) reported, at approximately the same time, very similar studies on the stability and electronic properties of a stanene/MoS2 heterobilayer using DFT. A band
gap was opened at the K point (slightly shifted in the case of Ren et al.) due to MoS2
breaking the symmetry of the sublattices of stanene (slightly bigger in the case of Xiong
et al. than in the other two reports). In the case of Liang et al. and Ren et al., the Dirac
cone was preserved, while Xiong et al. report on electron transfer from stanene to the substrate forming an internal electric field. The Dirac cone recovers upon applying an external field, equal to the internal one. The reason for the discrepancies may come from a different optimal interlayer spacing calculated, different stacking patterns as well as different functionals used in the calculations. All three reports conclude that the band gap can be effectively tuned with external strain and electric field. In the experimental field, although Chen et al. [58] report on forming multilayer stanene on MoS2. The
thickness of the deposited layer being 100 nm, poses a question if the name “stanene”, which refers to an atomic monolayer of the material, is used appropriately, as the experimental measurements in the paper are limited to TEM and XRD, while AFM images are not atomically resolved.
There are several more theoretical papers on different substrates, that are predicted to support stanene. Up to now however, there has been no experimental realization of stanene on any of them reported in the literature.
25 Table 2.I: Substrates on which stanene growth has been reported. In the columns respectively: a substrate, substrate general electronic properties, reconstruction, stanene lattice constant λ, buckling height Δ
Substrate Substrate Electr. Prop. Reconstructions λ[Å] Δ[Å] Source Bi2Te3 Topological insulator 1 x 1 4.4 3.5 [25] Free-standing No substrate 1 x 1 4.7 3.3 [34] Sb (111) semimetal 1 x 1 4.3 [24] Cu (111) metal 2 x 2 5.1 1.8 [33] InSb (111) semiconductor 1 x 1 4.58 2.85 [23] Bi (111) metal 1 x 1, √3 x √3R30 4.54 4 [32] MoS2 semiconductor 2.9 [58] Au (111) metal 2 x 2, √3 x √3, √3 x √7 -> 1 x 2 of stanene √7 5.1-5.7 2.4 2.4 [40] [31] Ag (111) metal √3 x √3 4.98 2.6 [30]
26
2.4.2 Substrates theoretically predicted to support epitaxial stanene
Hexagonal boron nitride (hBN), as an insulator with Van der Waals structure, was an obvious candidate for a stanene substrate. A theoretical study on the stability and the effect of strain was undertaken by Wang et al. [13] (see Fig. 2.4c ). They showed that stanene is stable on hBN and slightly compressed with respect to its freestanding form, which makes it semi-metallic. However, by application of an external strain, a QSHI phase can be induced. Additionally, the authors found another configuration with smaller lattice mismatch, which exhibits a QSHI phase without any strain. Another theoretical configuration was proposed in the paper of Wang et al. [59]. The result suggests that hBN can support stanene and preserve a topological gap. Khan et al. [60] also reported on a stanene/hBN heterobilayer in their theoretical work. The authors propose yet another stable configuration, in which the stanene layer is slightly stretched. The band structure of the Sn/hBN heterobilayer shows a direct band gap of about 30 meV at the Fermi energy, while the linear Dirac dispersion relation is maintained. Tensile strain and interlayer distance also have an impact on the band structure, showing that it is very prone to tuning. DFT studies on hexagonal nitrides (AlN, GaN, BN) as stanene substrates were also performed by Yelgel [61]. In the case of hBN, the author reported that the Dirac cone in monolayer stanene adsorbed on BN was preserved. The PDOS confirms previous claims that the carrier transport occurs only through the stanene layer. The biggest band gap was calculated in the case of stanene/GaN heterostructure. AlN shows strong interaction with the stanene layer, confirmed by previous reports.
The germanium ( Ge(111) ) surface was examined by Fang et al.[62] by means of DFT calculations (see Fig. 2.4b). They showed that stanene on Ge(111) has nontrivial topological phases. The Dirac cone exists around the Γ point, and the SOC open a band gap. In their report, El Bachra et al. [64] presented detailed calculations on stability, proving that buckled stanene is the preferable phase. They also suggested that there is a strong interaction between the Sn layer and the substrate. They confirmed that stanene preserves non-trivial topological features. While the theoretical field seem to paint a tempting landscape for further exploration, the experimental reports on Sn/Ge(111) heterostructures suggest that a Sn adlayer rather different from stanene is formed [65] [66].
27 Fig. 2.3: a) Stanene on SiC stack with corresponding calculated band structures with SOC. b) Stanene/MoS2 stack with the band structure with SOC. c) proposed atomic configuration of stanene on α-Al2O3 (0001) and their calculated band structures, including SOC. Figures adapted from a) [49] b) [57] c) [43].
An interesting idea is to combine two elemental 2D materials together. Chen et al. [67] explored that idea by investigating a stanene/graphene heterostructure. They studied structural, electronic and optical properties of several stacking configurations by means of DFT. They found interactions between the layers being stronger than typical Van der Waals bonds, which improves the stability of the system. In the case of some stacking configurations the system exhibits a Dirac feature in the vicinity of the K point. The authors suggest the tunability of the gap by means of an electric field. Finally, the system showed enhanced visible light absorption in all configurations. Wu et al. [63] performed similar calculations, additionally showing that multiple crystalline phases can coexist at room temperature (see Fig. 2.4a). They also suggest the possibility of tuning the electronic properties. Yun et al. [68] took a closer look on that aspect and calculated the behavior of the stanene/graphene system under strain and the influence of water vapor
28
adsorption. In their stability studies, they report an additional stacking configuration, not mentioned in previous studies. They concluded that the Fermi level can host Dirac or parabolic bands (or a mixture of both) depending on the strain and rotation. They also selected configurations in which a gap can be opened by application of external stress. The calculation on water vapor adsorption showed that it will modulate conductivity but not distort the band structure significantly. Another combination of stanene and graphene together was proposed by Mondal et al. [69] who proposed stanene sandwiched between two graphene layers. The structure exhibits a topologically protected hybrid state at the stanene-graphene interface, which is robust against severe strain.
The interests of Noshin et al. [70] were directed to another elemental 2D material – silicene. The authors examine a stanene/silicene bilayer by DFT. Their focus was on investigating thermal conductivity of the bilayer, and they showed that it has a thermal conductivity smaller than that of any other group IV elemental 2D material. Barhoumi
et al. [71] showed in their studies that a stanene/silicene bilayer is stable and the relaxed
structure is a direct band gap semiconductor.
Guo et al. [35] surveyed several metallic substrates using DFT, including aforementioned Ag, Au, Cu, Al, as well as Pd, Pt, Ir, and Ni. The stability of the honeycomb lattice was preserved, however buckling parameters changed, depending on the substrate. They also reported on the destruction of the stanene band structure and its metallization for all the substrates examined. Ding et al. [72] proposed InSe and GaTe as other candidates for stanene substrates. In their paper they calculated that stanene is stable on both of the substrates and preserves its Dirac cone as well as the SOC – induced band gap.
Zhang el al.[73] reported calculations on a functionalized stanene/ PbI2 heterostructure
as a suitable system for observing the quantum anomalous Hall effect (QAHE). The substrate is non-magnetic, therefore they induced ferromagnetism in the structure via functionalization of stanene. They also proposed a device comprising stanene sandwiched between PbI2 layers. In a follow – up paper [74] the group also showed that
the QSHE is present in the same structure. Ni et al. [75] investigated PbI2 and CaI2 by
means of DFT. They found both substrates to support stanene. While on PbI2 it exhibits
a trivial band gap, on CaI2 it is metallic, but external strain can open a non-trivial band
29 Chen et al. [76] investigated theoretically stanene on WS2. They examined the interlayer
distance, strain and the influence of an external electric field on the system. The system is stable, above a certain interlayer distance, and the electronic structure has a band gap with a Dirac cone at the K point. The authors further show that the size of the bandgap could be tuned with all the aforementioned parameters. Cao et al. [77] reported on their theoretical investigation on structural stability, as well as electronic and optical properties of a stanene/ZnO heterostructure. After finding the optimal interlayer distance, the electronic structure was determined to be metallic. A band gap can be opened however, by application of electric field and strain. They also showed that the system has potentially high UV absorption capability. Chakraborty et al. [78] investigated a stanene/BeO heterostructure. Its structural stability was confirmed, and electronic properties calculations showed a large band gap with Dirac cone opened, the size of which was enlarged by the interaction with the substrate.
30
Fig. 2.4: a) Stanene on graphene with band structures of (from the left) graphene, stanene and the whole system. b) Model of the stanene/Ge(111) heterostructure and the band structure (a) without and (b) with SOC. c) Stanene/hBN heterostructure with corresponding band structure without (left) and with (right) SOC. Figures reproduced from a) [63] b) [62] c) [13].
31 Table 2.II: Substrates proposed in DFT calculations. In the columns respectively: a substrate, substrate band gap given in the source article, reconstruction stack (stanene/substrate) used for calculations, an optimized interlayer distance d, lattice mismatch ε, buckling height Δ, band gap of the stanene/substrate system, topological Z2 invariant.
Substrate Egsubs (eV) reconstruction ε [%] d [Å] Δ [Å] Eg [meV] Z 2 source hBN 5 1 x 1 / √3 x √3 √7 x √7 / 5 x 5 3 x 3 / √31 x √31R9 2 x 2 / 4 x 4 2 x 2 / 4 x 4 6.9 1.5 0.25 7 6 3.30 3.3 3.7-3.8 3.4 up to 53 3 30 93 1 1 [13] [59] [60] [61] AlN 2.9 1x 1 / √3x √3 2x 2 /3x 3 2 x 2 / 3 x 3 19.5 3.4 1 2.70 >4.00 3 0.72 semimet. 63 [13] [61] Ge (111) 0.7 √3 x √3 /2 x 2 √3 x √3 /2 x 2 <1 1.5 3.2 1.4 34 1 [62] [64] InSe √3 x √3 /2 x 2 0.7 3.10 20 [72] GaTe √3 x √3 /2 x 2 2.2 3.45 80 [72] α-Al2O3 (0001) Ins. 1 x 1 / 1 x 1 1 x 1 / 1 x 1 3 2.7 2.88 2.7-2.9 0.7-1.2 250 260 1 [44] [43] Ag (111) - 7 x 7R19.107 / √19 x √19R23.42 4 x 4 / √43 x √43R7.6 3.3 2.7 2.41-2.48 2.49 1.06 metallic [36] [35]
32 1 x 1 / √3 x √3 4.38 1.81 Au (111) - 1 x 1 / √3 x √3 √7 x √7 / 3 x 3 4.27 1.15 1.63 metallic metallic [35] [39] Cu (111) Al (111) Pd (111) Pt (111) Ir (111) Ni (111) - 1 x 1 / √3 x √3 1 x 1 / √3 x √3 1 x 1 / √3 x √3 1 x 1 / √3 x √3 1 x 1 / √3 x √3 1 x √3R30/2 x 2√3R30 3.73 3.83 1.25 1.81 0.38 4.15 2.08 2.49 2.31 2.37 2.36 2.30 0.96 1.08 0 0 0.01 0 metallic [35] Graphene Graphene/ stanene/ graphene Graphene/ SiC - 2 x 2 / 4 x 4 √7 x √7R19.1 / 5x5 √7 x √7 / 5 x 5 1 x 1/ 2 x 2 1 x 1 / 2 x 2 √7 x √7R19.1 / 5 x 5 / 4 x 4 4.7 0.5 1.8 5.1 4.7 0.28 3.3 3.3 3.5-3.7 3.3-4 3.62 3.32 0.8 0.7-1.2 0.67 0.86 80 30 34 15 146 1 ? 1 ? [67] [63] [68] [69] [47] PbI2 *(I-passivated stanene) *Pristine stanene 2.5 1 x 1 1 x 1 0.4 1.3 3.2 3.16 0.87 0.89 300 30 1 0 [73] [74] [75] MoS2 1.8 2 x 2 / 3 x 3 2 x 2 / 3 x 3 1.28 1.45 3.2-3.4 3.1 0.85 72-77 67 [57] [55]
33 2 x 2 / 3 x 3 1.1 2.8 64 [56] CaI2 1 x 1 2.1 3.35 0.9 metallic * [75] WS2 1.8 2 x 2 / 3 x 3 1.9 3.00 0.85 62.9 [76] ZnO 1.7 2 x 2 / 3 x 3 3.3 3.00 0.78 metallic (60 at 3.2 A) [77] SiC SiC-H SiC-F SiC ML SiC (0001) 2.5 2 x 2 / 3 x 3 2 x 2 / 3 x 3 2 x 2 / 3 x 3 2 x 2 / 3 x 3 2 x 2 / 3 x 3 0.46 7.05 1 1 2.16 4.33 4.69 3.19-3.21 2.0-2.7 0.4-1.4 metallic 100 160 154-162 23 1 1 [46] [49] [50] Silicene 4 x 4 / 5 x 5 0.6 3.4 2.65 0.83 0.0 70-160 [70] [71] BeO 5.0 2 x 2 / 3 x 3 7 3.00 0.86 98 [78]
2.5 Conclusions
In summary, the field of stanene has many promises to realize and obstacles to overcome. The main promise is a QSHE at room temperature, and all the possible utilizations of that effect in various devices. The main obstacle is synthesis. The consensus in the community is that freestanding stanene is not possible to realize, and techniques that would support the growth on some kind of supporting structure are necessary. The main technique utilized so far in order to create stanene is epitaxial growth on a solid crystalline substrate. This review summarized the substrates examined by theoretical calculations for their feasibility of supporting a stanene layer. It also includes many up-to-date reports on experimental realizations of stanene-like single layers of Sn. This report thus serves as a useful “orientation point” for researchers that are new in the field.
34
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